Page:Popular Science Monthly Volume 69.djvu/558

554 I suppose that between the instants $$\alpha$$ and $$\beta$$ I have moved neither my body nor my eye, as I know from my muscular sense. Nor have I moved either my head, my arm or my hand. I ascertain that at the instant a impressions that I attributed to the object $$A$$ were transmitted to me, some by one of the fibers of my optic nerve, the others by one of the sensitive tactile nerves of my finger; I ascertain that at the instant $$\beta$$ other impressions which I attribute to the object $$B$$ are transmitted to me, some by this same fiber of the optic nerve, the others by this same tactile nerve.

Here I must pause for an explanation; how am I told that this impression which I attribute to $$A$$, and that which I attribute to $$B$$, impressions which are qualitatively different, are transmitted to me by the same nerve? Must we suppose, to take for example the visual sensations, that $$A$$ produces two simultaneous sensations, a sensation purely luminous $$a$$ and a colored sensation $$a'$$, that $$B$$ produces in the same way simultaneously a luminous sensation $$b$$ and a colored sensation $$b'$$, that if these different sensations are transmitted to me by the same retinal fiber, $$a$$ is identical with $$b$$, but that in general the colored sensations $$a'$$ and $$b'$$ produced by different bodies are different? In that case it would be the identity of the sensation $$a$$ which accompanies $$a'$$ with the sensation $$b$$ which accompanies $$b'$$, which would tell that all these sensations are transmitted to me by the same fiber.

However it may be with this hypothesis and although I am led to prefer to it others considerably more complicated, it is certain that we are told in some way that there is something in common between these sensations $$a+a'$$ and $$b+b'$$, without which we should have no means of recognizing that the object $$B$$ has taken the place of the object $$A$$.

Therefore I do not further insist and I recall the hypothesis I have just made: I suppose that I have ascertained that the impressions which I attribute to $$B$$ are transmitted to me at the instant $$\beta$$ by the same fibers, optic as well as tactile, which, at the instant $$\alpha$$, had transmitted to me the impressions that I attributed to $$A$$. If it is so, we shall not hesitate to declare that the point occupied by $$B$$ at the instant $$\beta$$ is identical with the point occupied by $$A$$ at the instant $$\alpha$$.

I have just enunciated two conditions for these points being identical; one is relative to sight, the other to touch. Let us consider them separately. The first is necessary, but is not sufficient. The second is at once necessary and sufficient. A person knowing geometry could easily explain this in the following manner: Let 0 be the point of the retina where is formed at the instant $$a$$ the image of the body $$A;$$ let $$M$$ be the point of space occupied at the instant $$a$$ by this body $$A;$$ let $$M$$ be the point of space occupied at the instant $$\beta$$ by the body $$B$$. For this body $$B$$ to form its image in 0, it is not necessary that the points $$M$$ and $$M'$$ coincide; since vision acts at a distance, it suffices for the